P, Q, R, S, T, U, and V live on seven different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is number 2, and so on up to the topmost floor numbered 7. Q lives on floor number 2. R lives on the floor immediately above U. S is on the floor immediately below V's floor. Only three persons live between the floors of T and P. R lives on the topmost floor. Only one person lives between the floors of R and P. On which floor does P live?

Explanation

Given Information: 1. Q lives on floor number 2. 2. R lives on the floor immediately above U. 3. S is on the floor immediately below V's floor. 4. There are three persons living between the floors of T and P. 5. R lives on the topmost floor (floor number 7). 6. Only one person lives between the floors of R and P. Step-by-Step Deduction: Since R is on the topmost floor (floor 7), we can write: Floor 7: R Since Q is on floor 2, we write: Floor 2: Q The only person who can live immediately below R (on floor 6) is U, so: Floor 6: U Therefore, RRR lives above UUU as mentioned. Now we know R is on floor 7 and U is on floor 6. We still need to place S and V. S is immediately below V, meaning if V is on floor nnn, then S is on floor n−1n- 1n−1. T and P must have three persons living between them. This means they cannot be on adjacent floors. The possible pairs for T and P (considering floors 1 to 7) could be: (1, 5), (2, 6), (3, 7) or their reverses. However, since QQQ is on floor 2, it rules out 2 for either T or P. Since R is on floor 7 and U is on floor 6, we can also determine the only possible positions for T and P: T can only be on floors 1, 3, or 4, leading to the following arrangements: If T is on 1, then P must be on 5. If T is on 3, then P must be on 7 (not possible since R is there). If T is on 4, then P must be on 1 (which is valid). However, since R is on floor 7, the only arrangement left would be if T were on floor 4 and P were on floor 1. With that arrangement, we can also place S and V. The only floor left is floor 3 for V, leading to S being on floor 2: Floor 1: P Floor 2: Q Floor 3: S Floor 4: T Floor 5: U Floor 6: V Floor 7: R Conclusion: From the deductions above, we can determine that P lives on floor 1.